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A fundamental effect of fluid turbulence is turbulent mixing, which resultsin the stretching and wrinkling of scalar isosurfaces. Thus, the area ofisosurfaces is of interest in understanding turbulence in general with specificapplications in, e.g., combustion and the identification ofturbulent/non-turbulent interfaces. We report measurements of isosurface areasin 28 direct numerical simulations (DNSs) of homogeneous isotropic turbulencewith a mean scalar gradient resolved on up to $14256^3$ grid points with TaylorReynolds number $Re{_\lambda}$ ranging from 24 to 633 and Schmidt number $Sc$ranging from 0.1 to 7. More precisely, we measure layers with very small butfinite thickness. The continuous equation we evaluate converges exactly to thearea in the limit of zero layer thickness. We demonstrate a method fornumerically integrating this equation that, for a test case with an analyticalsolution, converges linearly towards the exact solution with decreasing layerwidth. By applying the technique to DNS data and testing for convergence withresolution of the simulations, we verify the resolution requirements for DNSrecently proposed by \citet{yeung18}. We conclude that isosurface areas scalewith the square root of the Taylor P\'eclet number $Pe_{\lambda}$ betweenapproximately 50 and 4429 with some departure from power law scaling evidentfor $2.4 < Pe_{\lambda} < 50$. No independent effect of either $Re_{\lambda}$or $Sc$ is observed. The excellent scaling of area with $Pe_{\lambda}^{1/2}$occurs even though the probability density function (p.d.f.) of the scalargradient is very close to exponential for $Re_{\lambda}=98$ but approximatelylognormal when $Re_{\lambda}=633$.

Area of Scalar Isosurfaces in Homogeneous Isotropic Turbulence as a Function of Reynolds and Schmidt Numbers